U.S. President Barack Obama and Chinese President Xi Jinping walk the grounds at The Annenberg Retreat at Sunnylands in Rancho Mirage, California June 8, 2013 The two-day talks at a desert retreat near Palm Springs, California, was meant to be an opportunity for Obama and Xi to get to know each other, Chinese and U.S. officials have said, and to inject some warmth into often chilly relations while setting the stage for better cooperation.

U.S. President Barack Obama and Chinese President Xi Jinping concluded on Saturday their two days of informal meetings in southern California, and agreed on the need to denuclearize North Korea and fight global climate change, but the crucial issue of cybersecurity remains largely unresolved.

According to the White House, the meeting was aimed just at creating a more comfortable relationship between the two presidents, and Obama's national security adviser Tom Donilon sought to highlight that at a media briefing at the Westin Resort in Rancho Mirage, Calif., on Saturday.

Denying the notion that the world's largest economies are bound to have conflict, Donilon said, "We reject that and the Chinese government rejects that." Mydesert.com quoted him as saying, "The building out of this so-called new relationship – a new model of relations between great powers – is the effort to ensure that doesn't happen."

Xi, who took office in March, has lived in the U.S. briefly as a visiting official and his daughter also studied in the country. He and Obama appeared relaxed with each other.

Donilon, who is likely to be replaced by Susan Rice in July, said that resolving cybersecurity issues will be "key to the future" of the U.S.-China relations. The United States believes military-linked Chinese corporations have stolen military and economic information and property in cyberspace.

Donilon quoted Obama as telling Xi that "if it's not addressed, if it continues to be this direct theft of United States property, that this was going to be very difficult problem in the economic relationship and was going to be an inhibitor to the relationship really reaching its full potential," according to The Associated Press.

Obama, appearing with Xi on Friday night, told reporters, "Those are not issues that are unique to the U.S.-China relationship. Those are issues that are of international concern. Oftentimes it's non-state actors who are engaging in these issues as well."

Before the meetings, Obama also said he would reassure Xi that the United States is not trying to encircle China militarily. "This will give me an opportunity to reiterate how the United States welcomes the continuing peaceful rise of China as world power and that in fact it is in the United States' interest that China continues on the path of success."

Yang Jiechi, Xi's senior foreign policy adviser, was quoted as saying that "cybersecurity should not become the root cause of mutual suspicion and frictions between our two countries. Rather, it should be a new bright spot in our cooperation."

Meanwhile, the State Department said Friday that Beijing had agreed with the United States, Russia and other major nations at the United Nations that states' actions in cyberspace are under the purview of international law, according to The Washington Post.

The talks between Obama and Xi led to an agreement that they will not accept North Korea, which has conducted nuclear and missile tests this year, as a nuclear-armed state. "China has taken a number of steps in recent months to send a clear message to North Korea, including though enhanced enforcement of sanctions and through public statements by the senior leadership in China," Donilon said.

The White House said the two countries have also agreed to confront global climate change. "For the first time, the United States and China will work together and with other countries to use the expertise and institutions of the Montreal Protocol to phase down the consumption and production of hydrofluorocarbons (HFCs), among other forms of multilateral cooperation," it said in a statement.

While Obama has spoken about establishing "a new model of cooperation" with China, and Xi has called for "a new model of major country relations," many issues remain unresolved between the two nations, including arms sales to Taiwan, the South China Sea disputes and manipulation of the Chinese currency.

The Chinese president has invited his American counterpart to travel to China for another informal round of talks, even as the two leaders will likely meet again in September during an international economic summit in Russia.